# Amortized Bayesian Inference of GISAXS Data with Normalizing Flows

arXiv: https://arxiv.org/abs/2210.01543 · HTML: https://mlsanity.com/paper/2210.01543/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 28 references that are in the map.
- First posted on arXiv 4 Oct 2022.

## Builds on (most cited first, 8 of 8)

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Attribute2Image: Conditional Image Generation from Visual Attributes](https://mlsanity.com/paper/1512.00570/) (2015)
- [Scaling Up Machine Learning For Quantum Field Theory with Equivariant Continuous Flows](https://mlsanity.com/paper/2110.02673/) (2021)
- [Real-time coherent diffraction inversion using deep generative networks](https://mlsanity.com/paper/1806.03992/) (2018)
- [A neural simulation-based inference approach for characterizing the Galactic Center γ-ray excess](https://mlsanity.com/paper/2110.06931/) (2021)
- [Tracking perovskite crystallization via deep learning-based feature detection on 2D X-ray scattering data](https://mlsanity.com/paper/2202.10983/) (2022)

## Built on by (most cited first, 1 of 1)

- [Trustworthy scientific inference with generative models](https://mlsanity.com/paper/2508.02602/) (2025)

## Abstract (arXiv)

Grazing-Incidence Small-Angle X-ray Scattering (GISAXS) is a modern imaging technique used in material research to study nanoscale materials. Reconstruction of the parameters of an imaged object imposes an ill-posed inverse problem that is further complicated when only an in-plane GISAXS signal is available. Traditionally used inference algorithms such as Approximate Bayesian Computation (ABC) rely on computationally expensive scattering simulation software, rendering analysis highly time-consuming. We propose a simulation-based framework that combines variational auto-encoders and normalizing flows to estimate the posterior distribution of object parameters given its GISAXS data. We apply the inference pipeline to experimental data and demonstrate that our method reduces the inference cost by orders of magnitude while producing consistent results with ABC.